Reed-Solomon codes are used in a variety of applications including optical and magnetic storage devices, satellite communications, and compact disk recording. In some of these applications, Reed-Solomon codes are implemented as a hardware device, such as an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA). The decoder is typically much larger and more computation intensive than the encoder. In hardware and non-hardware implementations, improved Reed-Solomon decoders (for example, with reduced hardware or reduced latency) may be useful to systems that employ such devices.